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The influence of material non-uniformity preceding shear-band formation in a model for granular flow

Published online by Cambridge University Press:  01 October 1997

DAVID G. SCHAEFFER  and
MICHAEL SHEARER
DAVID G. SCHAEFFER
Affiliation:
Department of Mathematics, Duke University, Durham, NC 27708-0320, USA
MICHAEL SHEARER
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA
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Abstract

The onset of shear-banding in a deforming elastoplastic solid has been linked to change of type of the governing partial differential equations. If uniform material properties are assumed, then (i) deformations prior to shear-banding are uniform, and (ii) the onset of shear-banding occurs simultaneously at all points in the sample. In this paper we study, in the context of a model for anti-plane shearing of a granular material, the effect of a small variation in material properties (e.g. in yield strength) within the sample. Using matched asymptotic expansions, we find that (i) the deformation is extremely non-uniform in a short time period immediately preceding the formation of shear-bands; and (ii) generically, a shear-band forms at a single location in the sample.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 8 , Issue 5 , October 1997 , pp. 457 - 483
Copyright
© 1997 Cambridge University Press

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